arXiv subjects

Fabio Cecconi

Publications and source records attributed to Fabio Cecconi.

52 records · Page 3Linked to original sources

arXiv2005

Brownian motion and diffusion: from stochastic processes to chaos and beyond

One century after Einstein's work, Brownian Motion still remains both a fundamental open issue and a continous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic approaches proposed in the literature to model the Brownian Motion and more general diffusive behaviours. Then, we focus on the problems concerning the determination of the microscopic nature of diffusion by means of data analysis. Finally, we discuss the general conditions required for the onset of large scale diffusive motion.

nlin.CD↗

arXiv2005

Functional Dynamics of PDZ Binding Domains: A Normal Mode Analysis

PDZ (Post-synaptic density-95/discs large/zonula occludens-1) domains are relatively small (80 to 120 residues) protein binding modules central in the organization of receptor clusters and in the association of cellular proteins. Their main function is to bind C-terminals of selected proteins that are recognized through specific amino-acids in their carboxyl end. Binding is associated with a deformation of the PDZ native structure and is responsible for dynamical changes in regions not in direct contact with the target. We investigate how this deformation is related to the harmonic dynamics of the PDZ structure and show that one low-frequency collective normal mode, characterized by the concerted movements of different secondary structures, is involved in the binding process. Our results suggest that even minimal structural changes are responsible of communication between distant regions of the protein, in agreement with recent Nuclear Magnetic Resonance (NMR) experiments. Thus PDZ domains are a very clear example of how collective normal modes are able to characterize the relation between function and dynamics of proteins, and to provide indications on the precursors of binding/unbonding events.

q-bio.BM↗

arXiv2005

Models of fluidized granular materials: examples of non-equilibrium stationary states

We review some models of granular materials fluidized by means of external forces such as: random homogeneous forcing with damping, vibrating plates, flow in an inclined channel and flow in a double well potential. All these systems show the presence of density correlations and non-Gaussian velocity distributions. These models are useful to understand the role of a kinetically defined ``temperature'' (in this case the so-called {\em granular temperature}) in a non-equilibrium stationary state. In the homogeneously randomly driven gas the granular temperature is {\em different} from that of the driving bath. Moreover two different granular materials mixed together may stay in a stationary state with different temperatures. At the same time, granular temperature determines (as in equilibrium systems) the escape time from a well in a double well potential.

cond-mat.soft↗

arXiv2005

Analysis of PIN1 WW domain through a simple Statistical Mechanics Model

We have applied a simple statistical-mechanics G$\bar{\text{o}}$-like model to the analysis of the PIN1 WW domain, resorting to Mean Field and Monte Carlo techniques to characterize its thermodynamics, and comparing the results with the wealth of available experimental data. PIN1 WW domain is a 39-residues protein fragment which folds on an antiparallel $β$-sheet, thus representing an interesting model system to study the behavior of these secondary structure elements. Results show that the model correctly reproduces the two-state behavior of the protein, and also the trends of the experimental $ϕ_T$-values. Moreover, there is a good agreement between Monte Carlo results and the Mean-Field ones, which can be obtained with a substantially smaller computational effort.

physics.bio-ph↗

arXiv2004

Inelastic hard-rods in a periodic potential

A simple model of inelastic hard-rods subject to a one-dimensional array of identical wells is introduced. The energy loss due to inelastic collisions is balanced by the work supplied by an external stochastic heat-bath. We explore the effect of the spatial non uniformity on the steady states of the system. The spatial variations of the density, granular temperature and pressure induced by the gradient of the external potential are investigated and compared with the analogous variations in an elastic system. Finally, we study the clustering process by considering the relaxation of the system starting from a uniform homogeneous state.

cond-mat.mtrl-sci↗

arXiv2004

Minimal Stochastic Model for Fermi's Acceleration

We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through a linear Boltzmann equation. The asymptotic probability distribution functions (PDF) for velocity and position are explicitly derived. The diffusion process is highly non-Gaussian and the time growth of moments is characterized by only two exponents $ν_x$ and $ν_v$. The diffusion process is anomalous (non Gaussian) but with a defined scaling properties i.e. $P(|{\bf x}|,t) = 1/t^{ν_x}F_x(|{\bf x}|/t^{ν_x})$ and similarly for velocity.

cond-mat.stat-mech↗

arXiv2003

Fluid-like behavior of a one-dimensional granular gas

We study the properties of a one-dimensional (1D) granular gas consisting of $N$ hard rods on a line of length $L$ (with periodic boundary conditions). The particles collide inelastically and are fluidized by a heat bath at temperature $T_b$ and viscosity $γ$. The analysis is supported by molecular dynamics simulations. The average properties of the system are first discussed, focusing on the relations between granular temperature $T_g=m< v^2>$, kinetic pressure and density $ρ=N/L$. Thereafter, we consider the fluctuations around the average behavior obtaining a slightly non-Gaussian behavior of the velocity distributions and a spatially correlated velocity field; the density field displays clustering: this is reflected in the structure factor which has a peak in the $k \sim 0$ region suggesting an analogy between inelastic hard core interactions and an effective attractive potential. Finally, we study the transport properties, showing the typical sub-diffusive behavior of 1D stochastically driven systems, i.e. $<|x(t)-x(0)|^2 > \sim Dt^{1/2}$ where $D$ for the inelastic fluid is larger than the elastic case. This is directly related to the peak of the structure factor at small wave-vectors.

cond-mat.stat-mech↗

arXiv2003

Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model

We study the asymptotic behaviour of the Bak, Tang, Wiesenfeld sandpile automata as a closed system with fixed energy. We explore the full range of energies characterizing the active phase. The model exhibits strong non-ergodic features by settling into limit-cycles whose period depends on the energy and initial conditions. The asymptotic activity $ρ_a$ (topplings density) shows, as a function of energy density $ζ$, a devil's staircase behaviour defining a symmetric energy interval-set over which also the period lengths remain constant. The properties of $ζ$-$ρ_a$ phase diagram can be traced back to the basic symmetries underlying the model's dynamics.

cond-mat.stat-mech↗

arXiv2003

Complexity Characterization of Dynamical Systems Through Predictability

Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a characterization of the unpredictability of a system gives a measure of its complexity. A special attention is devoted to finite-resolution effects on predictability, which can be accounted with suitable generalization of the standard indicators. The problems involved in systems with intrinsic randomness is discussed, with emphasis on the important problems of distinguishing chaos from noise and of modeling the system.

nlin.CD↗

arXiv2003

The origin of diffusion: the case of non chaotic systems

We investigate the origin of diffusion in non-chaotic systems. As an example, we consider 1-$d$ map models whose slope is everywhere 1 (therefore the Lyapunov exponent is zero) but with random quenched discontinuities and quasi-periodic forcing. The models are constructed as non-chaotic approximations of chaotic maps showing deterministic diffusion, and represent one-dimensional versions of a Lorentz gas with polygonal obstacles (e.g., the Ehrenfest wind tree model). In particular, a simple construction shows that these maps define non-chaotic billiards in space-time. The models exhibit, in a wide range of the parameters, the same diffusive behavior of the corresponding chaotic versions. We present evidence of two sufficient ingredients for diffusive behavior in one-dimensional, non-chaotic systems: i) a finite-size, algebraic instability mechanism, and ii) a mechanism that suppresses periodic orbits.

nlin.CD↗

arXiv2003

Mean Field Approach for a Statistical Mechanical Model of Proteins

We study the thermodynamical properties of a topology-based model proposed by Galzitskaya and Finkelstein for the description of protein folding. We devise and test three different mean-field approaches for the model, that simplify the treatment without spoiling the description. The validity of the model and its mean-field approximations is checked by applying them to the $β$-hairpin fragment of the immunoglobulin-binding protein (GB1) and making a comparison with available experimental data and simulation results. Our results indicate that this model is a rather simple and reasonably good tool for interpreting folding experimental data, provided the parameters of the model are carefully chosen. The mean-field approaches substantially recover all the relevant exact results and represent reliable alternatives to the Monte Carlo simulations.

cond-mat.soft↗

arXiv2003

Noise activated granular dynamics

We study the behavior of two particles moving in a bistable potential, colliding inelastically with each other and driven by a stochastic heat bath. The system has the tendency to clusterize, placing the particles in the same well at low drivings, and to fill all of the available space at high temperatures. We show that the hopping over the potential barrier occurs following the Arrhenius rate, where the heat bath temperature is replaced by the granular temperature. Moreover, within the clusterized ``phase'' one encounters two different scenarios: for moderate inelasticity, the jumps from one well to the other involve one particle at a time, whereas for strong inelasticity the two particles hop simultaneously.

cond-mat.stat-mech↗

arXiv2002

Crucial stages of protein folding through a solvable model: predicting target sites for enzyme-inhibiting drugs

An exactly solvable model based on the topology of a protein native state is applied to identify bottlenecks and key-sites for the folding of HIV-1 Protease. The predicted sites are found to correlate well with clinical data on resistance to FDA-approved drugs. It has been observed that the effects of drug therapy are to induce multiple mutations on the protease. The sites where such mutations occur correlate well with those involved in folding bottlenecks identified through the deterministic procedure proposed in this study. The high statistical significance of the observed correlations suggests that the approach may be promisingly used in conjunction with traditional techniques to identify candidate locations for drug attacks.

cond-mat.stat-mech↗

arXiv2002

Diffusion, peer pressure and tailed distributions

We present a general, physically motivated non-linear and non-local advection equation in which the diffusion of interacting random walkers competes with a local drift arising from a kind of peer pressure. We show, using a mapping to an integrable dynamical system, that on varying a parameter, the steady state behaviour undergoes a transition from the standard diffusive behavior to a localized stationary state characterized by a tailed distribution. Finally, we show that recent empirical laws on economic growth can be explained as a collective phenomenon due to peer pressure interaction.

cond-mat.stat-mech↗

arXiv2001

Molecular Dynamics Studies on HIV-1 Protease: Drug Resistance and Folding Pathways

Drug resistance to HIV-1 Protease involves accumulation of multiple mutations in the protein. Here we investigate the role of these mutations by using molecular dynamics simulations which exploit the influence of the native-state topology in the folding process. Our calculations show that sites contributing to phenotypic resistance of FDA-approved drugs are among the most sensitive positions for the stability of partially folded states and should play a relevant role in the folding process. Furthermore, associations between amino acid sites mutating under drug treatment are shown to be statistically correlated. The striking correlation between clinical data and our calculations suggest a novel approach to the design of drugs tailored to bind regions crucial not only for protein function but also for folding.

cond-mat.stat-mech↗

arXiv1999

Nonequilibrium Phase Transition in Non-Local and Nonlinear Diffusion Model

We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals. We study a dynamical phase transition that is obtained on tuning the initial conditions and demonstrate universality and characterize the critical behavior. The critical state is shown to be reached in a self-organized manner on dynamically evolving the diffusion equation subjected to a mirror symmmetry transformation.

cond-mat.stat-mech↗